Monad metrizable space

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Mathematics, cilt.8, sa.11, ss.1-14, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 11
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3390/math8111891
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-14
  • Anahtar Kelimeler: Amply soft monad point, Amply soft set, AS topology, Monad metric space, Monad metrizable space, Parametric separation axioms, PAS metric space, PAS topology, Pi,i = 0, 1, 2, 3, 4, Soft metric space, Soft set theory
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

© 2020 by the author. Licensee MDPI, Basel, Switzerland.Do the topologies of each dimension have to be same and metrizable for metricization of any space? I show that this is not necessary with monad metrizable spaces. For example, a monad metrizable space may have got any indiscrete topologies, discrete topologies, different metric spaces, or any topological spaces in each different dimension. I compute the distance in real space between such topologies. First, the passing points between different topologies is defined and then a monad metric is defined. Then I provide definitions and some properties about monad metrizable spaces and PAS metric spaces. I show that any PAS metric space is also a monad metrizable space. Moreover, some properties and some examples about them are presented.